in a word, no. a petition of 5000 is given zero consideration if the arguments it is based on are not relevant in planning terms. one person's letter raising salient planning-relevant points is far more powerful. that's the way things are at present in planning but funnily enough I think the Tories are trying to change that in England to allow more middle class nimbyism.
the actual Councillors (who I assume made the final decision here, based upon the Council Officer's recommendation for approval in all likelihood) would have been in a better position to refuse on more dubious grounds though (i.e. found an excuse to refuse. and it surprises me that they didn't).
worth remembering too that the planning permission wasn't granted for a Tesco Express, but simply for a medium sized shop (albeit one with Tesco Express signage).